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A three-variable model of deterministic chaos in the Belousov–Zhabotinsky reaction

Nature volume 355, pages 808–810 (1992)Cite this article

Abstract

CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws1–3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov–Zhabotinsky (BZ) reaction4–6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator7 (which cannot produce chaos).

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Authors and Affiliations

  1. Department of Chemistry, University of Montana Missoula, Montana, 59812, USA

    László Györgyi & Richard J. Field

  2. Institute of Inorganic and Analytical Chemistry Eotvos Lorand University, Budapest-112, PO Box 32, H-1518, Hungary

    László Györgyi

Authors
  1. László Györgyi
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  2. Richard J. Field
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Györgyi, L., Field, R. A three-variable model of deterministic chaos in the Belousov–Zhabotinsky reaction. Nature 355, 808–810 (1992). https://doi.org/10.1038/355808a0

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